I have a Whirlpool RBS245PDQ12 wall mount oven. Gathering information from AppliancePartsPros.com resulted in two possibilities: The Thermal Switch or the Control Panel. Talking with Appliance Parts Pros led to testing the Oven Temperature Sensor. It's supposed to test at 1080 Ohms at 70 degrees Fahrenheit. Mine tested at 960 Ohms so I knew it was bad... I found the service manual on the top of the Oven on the left behind the control panel. It has values for testing (Ohms of resistance) and other test procedures. It details how to test the Thermal Switch. I did that and the Thermal Switch tested good. The oven would not of course work after I replaced the Oven Temperature Sensor which I ordered from Appliance Parts Pros but I knew I needed to buy it because it tested out of specification. Here's what the actual repair was: Back in the 90's there was a lot of high Tin content solder that was used. The connectors that plug onto the Control Panel connect to long pins that are soldered on the Control Panel. I examined the solder joints and every one of them had cracked solder. I melted the solder and removed it with a solder sucker which is a nifty tool for removing solder. Then I resoldered everything on the board that was bad. The way you can find this problem is to remove your Control Panel and use a magnifying glass to examine the solder joints and look for any that are cracked. This is probably what repair shops are doing with these vintage Control Boards. After redoing the solder joints I plugged the connectors back onto the Control Board and everything lit up and worked normally.
So here's your best procedure: If the oven won't work because the control panel is dead or if it displays "PF" every time you touch the control panel then the solder joints are likely broken. The other possibility is that the oven got way too hot and the Thermal Switch tripped. In that case, you will find the procedure for testing the Thermal Switch and you will find it open circuit because when a Thermal Switch goes open it's bad and stays that way. Those are the ONLY two things that will make the control panel not function (no display) unless the display driver circuit fails on the control panel. You will also find procedures to check and program your oven in the manual (If you don't have the manual for the oven then find it on the Internet). The control panel can be programmed for what size the oven is and also what the temperature OFFSET is. These ovens can be set for an offset of up to -30 F to + 30 F. That means you can make your oven up to 30 F hotter or cooler than what the temperature says on the display. By the way, if you put everything back together and the display says "LOC" then hold down the START button for 10 seconds, then the display will say "OFF" so you press the off button once and the control panel returns to normal operation... And have fun because it's just an oven and new ones are only an incredible amount of money. Appliance Parts Pros are good people in my opinion and they honestly do work toward solving your problem.